[TeMPOraL]

Computers can become non-deterministic in practice as soon as you botch your random number handling, or hook your input up to environmental noise. Is there anything suggesting the brain is non-deterministic in a theoretical way, not just the way computers are?

[vinceguidry]

Deterministic means that given the same input, the system gives the same output. Computers would be useless if they were not deterministic. Hooking up random input to a deterministic process will give random output. Garbage in, garbage out.

What you're asking is for computers to be rational. That given garbage input, it will produce intelligible output. Computers cannot do this unless you program them to.

Human minds are non-deterministic in many, many, many ways. Hand the same input to the same mind and you'll get a different output every single time, unless the mind willed itself to act rationally. But they are deterministic enough that you can study their behavior. Other brains are not as non-deterministic, so their behavior is easier to study.

Look at it from a thermodynamic standpoint. Biological systems arose to conserve order against entropy. A fully-deterministic system will shed order, it's only through non-deterministic means that biological systems can conserve order.

The mind is the most complex system nature has devised that can not only slow the aggregation of entropy, but also create order! It's not breaking the laws of physics, but yet it can create all kinds of order.

Conway's Game of Life is an excellent illustration of the concept. You have to work hard and study the domain in order to find stable systems. Otherwise they just drop to equilibrium fast.

[TeMPOraL]

Thermodynamics is defined in a deterministic universe. It's only through sheer amount of states any interesting system could be in that entropy arises. Chaotic systems (as studied in mathematics) are deterministic too. Conway's Game of Life is indeed an excellent illustration of the concept - of how chaotic and "surprising" behavior can arise in a fully deterministic system.

> Human minds are non-deterministic in many, many, many ways. Hand the same input to the same mind and you'll get a different output every single time

That's not non-deterministic. That's simply stateful. Most human-made systems you interact with daily are stateful, so it's not exactly surprising.

When I say "deterministic in practice" vs. "deterministic in theory" I mean this: a system is deterministic in practice if you can actually predict its outputs based on its inputs with reasonable amount of effort. A LED hooked up to a switch and a battery is deterministic in practice. So is a program computing GCD on 32-bit integers. A system is deterministic in theory if it's deterministic, but actually predicting its outputs requires absurd amount of computation. Lorenz system and weather are two examples. So is protein folding and turbulent flow. I see no reason why a fly brain, a mouse brain, or a human brain wouldn't be such systems either. The entire universe could be one, if you subscribe to many-worlds interpretation of quantum mechanics.

[vinceguidry]

> I mean this: a system is deterministic in practice if you can actually predict its outputs based on its inputs with reasonable amount of effort.

You're changing the meaning of determinism and bringing it closer to rationalism. Your introduction of the element of theory to the mix is a violation of Occam's Razor. We already have philosophy and a word that covers what you want it to cover. Theory is a component of rationalism, not of determinism. If you need theory to understand a system, then it already has elements of non-determinism. Theory is what you need to make sense of the non-deterministic. Because theory deals with uncertainty, you wouldn't need any validation of your hypotheses if the system was truly deterministic. One observation would be enough to ascertain the whole thing.

A considered study of history would reveal where you're going wrong here. The Greeks invented empiricism and philosophy and science while the Egyptians never got there despite only being a tiny distance away. They wanted to distance themselves from theological frames. Despite all this, the Egyptians built pyramids. They understood determinism. They could not understand science. Determinism made them good engineers. Engineering is not science.

> A system is deterministic in theory if it's deterministic, but actually predicting its outputs requires absurd amount of computation.

Now you're starting to dip into computational complexity territory. Predicting outputs is the domain that the halting problem puts a backstop to.

To prove to you that a brain is better than a computer, all I have to do is state the obvious, humans make algorithms, not the other way around. Sure, there are programs that will devise algorithms, but humans have to understand the domain before they can make computers do their work for them.

Your examples of Lorenz systems and weather do not change things at all. Humans have a better understanding of weather than computers do. In fact, humans have an entire body of theory that attempts to make sense of why such things have difficult-to-determine causation, chaos theory. Humans devised it, not computers. And they devised it using the tools of epistemology, working out the details of justification of knowledge via seeking rigor, not in the scientific method of dreaming up hypotheses based on empirical analysis and testing them. Chaos theory is more math than science.

In other real ways, humans outclass other mammals, even though we largely share the same macro brain structures. We keep monkeys in cages, monkeys do not keep us in cages.

I'm not sure how much more I have to state the obvious here. You seem to be the one seeking out a special domain in which the rules don't apply, one in which computers are wholly analogous to brains. It may, and this is speculation, be true in degree rather than kind.

But the halting problem itself illustrates a domain in which humans are able to reason past, whereas we cannot possibly program a computer to do it. Computers cannot program themselves to find gradations of the halting problem. Humans have to write algo-generating algos. The pace of comp-sci progress at the moment is fully dictated by human ingenuity, and if you think about it, any change in this means that the singularity is upon us.

I suspect that we'll never be able to get computers to fully take the place of brains. There will always be domains where brains are better than algos. Prove me wrong. Humans are capable of wanting things, even the best machine learning algos at the moment struggle with finding purpose. Finding purpose is something even the most basic virus can achieve. And we can't even determine whether virii are alive or not.

And that's super basic. How much more self-awareness do you think algos can find before running into hard physical limits? The computational and memory concerns are huge. I predict the hard limit of engineered systems will be well below full self-awareness. Instead we'll have to create biological systems to carry on progress. Dogs will get smarter, mice will get smarter, apes will eventually start doing things that humans do now, once we can fit our ethics around it.

[ryukafalz]

>Hand the same input to the same mind and you'll get a different output every single time, unless the mind willed itself to act rationally.

Are you sure? Remember that memory also counts as an input if it's used in a computation; it seems to me that this applies to both humans and computers.

For a harrowing account of what a mind may do when exposed to very nearly the same inputs, you may be interested in one segment from this Radiolab episode: https://www.wnycstudios.org/story/radiolab-loops

It describes a patient with transient global amnesia who has a looping conversation with her daughter. (There's a link to a video of the conversation on that page as well.) Under normal circumstances this wouldn't happen, as once you've had a conversation you also have memories of having that conversation. But if you're unable to form memories...